High-precision positioning with global navigation satellite systems (GNSS) remains a significant challenge in urban environments, due to the outliers caused by the insufficient number of accessible satellites and environmental interference. A GNSS outlier mitigation algorithm with effective fault detection and exclusion (FDE) is required for high-precision positioning. The traditional methods are designed to deal with zero-mean noise in GNSS, which leads to instabilities under biased measurements. Considering that GNSS data are typical time series data, a dynamic FDE scheme is constructed by combining a prediction-model-based method and a dissimilarity-based method. First, a hybrid prediction model which combines autoregressive integrated moving average (ARIMA) model and multilayer perceptron (MLP) model is proposed to provide pseudo-GNSS series by predicting the vehicle’s location for several future steps. Then, a dissimilarity-based method of dynamic time warping measure is utilized to analyze the pairwise dis-similarity between the pseudo-GNSS series and the received GNSS series. The performance of the different models in forecasting is evaluated, and the results show that the positioning accuracy is significantly improved by applying the ARIMA-MLP. The effectiveness of the proposed FDE method is verified through simulation experiments and real experiments based on a typical urban canyon public dataset collected in Tokyo.